Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
# IAWT
n, m = list(map(int, input().split()))
g = [list(map(int, input().split())) for i in range(n)]

class Phrase: # xa + y
    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y
    def __add__(self, other):
        return Phrase(self.x+other.x, self.y+other.y)
    def __str__(self):
        return str(self.x)+'a'+' + '+str(self.y)

    
class Equ: # left = right
    def __init__(self, a, b):
        self.left = a
        self.right = b

    def solve(self):
        if self.left.x == self.right.x and self.left.y == self.right.y:
            return 'infinity'
        self.left.x -= self.right.x
        self.right.x = 0
        self.right.y -= self.left.y
        self.left.y = 0
        if self.left.x == 0 and self.right.y != 0:
            return 'nothing'
        return self.right.y / self.left.x

mina, maxa = 0, 1000
rows = []
for i in range(n):
    new = Phrase(-1, g[i][0])
    rows.append(new)
    if new.x < 0: maxa = min(maxa, new.y / -(new.x))
    if new.y < 0: mina = max(-(new.y) / new.x, mina)

def f():
    global exact, mina, maxa, cols, rows, a, s, i, u, s2
    exact = ''
    cols = [Phrase(1, 0)]
    for i in range(1, m):
        last = Phrase(-rows[0].x, -rows[0].y + g[0][i])
        cols.append(last)
        if last.x < 0 and last.y < 0: print(-1); return
        if last.x < 0: maxa = min(maxa, last.y / -(last.x))
        if last.y < 0: mina = max(-(last.y) / last.x, mina)
        for u in range(1, n):
            new = Phrase(-rows[u].x, -rows[u].y + g[u][i])
            rslt = Equ(last, new).solve()
            if rslt == 'nothing':
                print(-1)
                return
            if rslt == 'infinity':
                last = new
                continue
            if new.x < 0 and new.y < 0: print(-1); return
            if new.x < 0: maxa = min(maxa, new.y / -(new.x))
            if new.y < 0: mina = max(-(new.y) / new.x, mina)
            if rslt % 1 != 0:
                print(-1)
                return
            if exact == '': exact = rslt
            elif rslt != exact:
                print(-1)
                return

    if mina % 1 != 0:
        mina = int(mina)+1
    maxa = int(maxa)
    if maxa < mina:
        print(-1)
        return
    if exact != '':
        if exact > maxa or exact < mina:
            print(-1)
            return
        a = exact
        for i in range(m):
            for u in range(n):
                s = rows[i].x * a + rows[i].y + cols[u].x * a + cols[u].y
                if s != g[u][i]:
                    print(-1)
                    return
        
        for i in range(m):
            cols[i] = cols[i].x * a + cols[i].y
            if cols[i] % 1 != 0:
                print(-1)
                return
            cols[i] = int(cols[i])
        for i in range(n):
            rows[i] = rows[i].x * a + rows[i].y
            if rows[i] % 1 != 0:
                print(-1)
                return
            rows[i] = int(rows[i])
        s = sum(cols) + sum(rows)
        print(s)
        for i in range(m):
            for u in range(cols[i]):
                print('col', i+1)
        for i in range(n):
            for u in range(rows[i]):
                print('row', i+1)
        return
    else:
        s2 = Phrase()
        for i in range(m): s2 += cols[i]
        for i in range(n): s2 += rows[i]
        if s2.x < 0: a = maxa
        else: a = mina
        
        for i in range(m):
            cols[i] = cols[i].x * a + cols[i].y
            if cols[i] % 1 != 0:
                print(-1)
                return
            cols[i] = int(cols[i])
        for i in range(n):
            rows[i] = rows[i].x * a + rows[i].y
            if rows[i] % 1 != 0:
                print(-1)
                return
            rows[i] = int(rows[i])
        s = sum(cols) + sum(rows)
        print(s)
        for i in range(m):
            for u in range(cols[i]):
                print('col', i+1)
        for i in range(n):
            for u in range(rows[i]):
                print('row', i+1)
        return
f()